HENDERSON, Nev. — Republican presidential nominee Mitt Romney sought Tuesday to deepen the sense of momentum that his campaign is seeking to project since polls tightened earlier this month.

“These debates have supercharged our campaign,” Romney declared at his first rally since the final debate with President Barack Obama Monday night. “There’’s no question about it, we’re seeing more and more enthusiasm, more and more support.”

Romney assailed Obama for failing to offer an affirmative vision for the next four years — a charge the president’s campaign has been sensitive to, releasing a 20-page booklet on his agenda for the next four years just this morning. “Well you know,” Romney said, “[Obama’s] been reduced to try to defend characters on Sesame Street and word games of various kinds, and then misfired attacks after one and another.”

“The truth is, attacks on me are not an agenda,” Romney said, repeating one of his strongest lines from the foreign policy debate. “The President — we’ve gone through four debates now — we’ve gone through four debates: the vice presidential debate and my debates, and we haven’t heard an agenda from the president.”

Exuding confidence is a time-honored and necessary part of running for president, but Romney had in fact avoided making the — until October risible — claim that he was on track to victory. He finally arrived at that posture Tuesday afternoon at an outdoor rally before thousands of enthusiastic fans outside Las Vegas.

“That’s why his campaign is taking on water, and our campaign is full speed ahead,” he added, recognizing his surge in statewide and national polling to a neck-and-neck position with Obama.

“His campaign is slipping, and ours is gaining so much steam,” he later added triumphantly in his freshly-polished stump speech, describing his campaign for the first time “as a movement across the country.”